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"m1aFRP"}], ")"}], "+", RowBox[{"(", RowBox[{"1", "/", "m2aFRP"}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "/", "m1bFRP"}], ")"}], "+", RowBox[{"(", RowBox[{"1", "/", "m2bFRP"}], ")"}]}], ")"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.6750574802879047`*^9, 3.6750575833758006`*^9}}], Cell["\<\ The acoustic phonon close to k=0 is nearly zero anyway due to a k vector \ dependence\ \>", "Text", CellChangeTimes->{{3.675057592127301*^9, 3.6750576156066437`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Optical at \[Pi] k, zone boundary", "Subsubsection", CellChangeTimes->{{3.675057660550215*^9, 3.6750576793192883`*^9}}], Cell[TextData[{ "If we go to the Brillouin zone boundary for the same lattice, we find the \ motion to be:\n", Cell[BoxData[ FormBox[ RowBox[{"\[Omega]", "\[TildeTilde]", SqrtBox[ FractionBox[ RowBox[{"2", "C"}], SubscriptBox["M", "2"]]]}], TraditionalForm]]], "\nThe ratio is then ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ SubscriptBox["\[Omega]", "A"], SubscriptBox["\[Omega]", "B"]], "\[TildeTilde]", SqrtBox[ FractionBox[ SubscriptBox["M", RowBox[{"2", ",", "B"}]], SubscriptBox["M", RowBox[{"2", ",", "A"}]]]]}], TraditionalForm]]], "if the force constants are similar. \n", Cell[BoxData[ FormBox[ SubscriptBox["M", "1"], TraditionalForm]]], " seems to be heavier usually, because then the phonon branches don\ \[CloseCurlyQuote]t cross.\nSo this would be simply the root of the ratio of \ the anion mass in our case?" }], "Text", CellChangeTimes->{{3.6750576868077164`*^9, 3.675057864372873*^9}, { 3.675057902333044*^9, 3.675057953716983*^9}, {3.6750579977805033`*^9, 3.6750580238759956`*^9}, {3.7022854533023434`*^9, 3.702285458885663*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"freqratioPOPI", "[", RowBox[{"m2aFRPP_", ",", "m2bFRPP_"}], "]"}], ":=", RowBox[{"Sqrt", "[", RowBox[{"m2bFRPP", "/", "m2aFRPP"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.675057871805298*^9, 3.675057898628832*^9}, { 3.6750581335232673`*^9, 3.6750581575796432`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Acoustic at \[Pi] k, zone boundary", "Subsubsection", CellChangeTimes->{{3.675057660550215*^9, 3.6750576793192883`*^9}, { 3.675057753502531*^9, 3.6750577578697815`*^9}}], Cell[TextData[{ "If we go to the Brillouin zone boundary for the same lattice, we find the \ motion to be:\n", Cell[BoxData[ FormBox[ RowBox[{"\[Omega]", "\[TildeTilde]", SqrtBox[ FractionBox[ RowBox[{"2", "C"}], SubscriptBox["M", "1"]]]}], TraditionalForm]]], "\nThe ratio is then ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ SubscriptBox["\[Omega]", "A"], SubscriptBox["\[Omega]", "B"]], "\[TildeTilde]", SqrtBox[ FractionBox[ SubscriptBox["M", RowBox[{"1", ",", "B"}]], SubscriptBox["M", RowBox[{"1", ",", "A"}]]]]}], TraditionalForm]]], "if the force constants are similar\nWe probably wouldn\[CloseCurlyQuote]t \ see a shift in those then, because the heavier cations are extremely similar \ in mass.\nIt would be in line with the fact that our methods should excite \ only the optical phonons in zerost approximation due to the interaction of \ the motion with the electrical field. Acoustic modes would not have the \ charge displacement to do that.\nAcoustic phonon in the middle goes to zero \ because of the k vector dependence." }], "Text", CellChangeTimes->{{3.6750576868077164`*^9, 3.675057761662998*^9}, { 3.675057826069682*^9, 3.675057826069682*^9}, {3.675057973836134*^9, 3.6750579819805994`*^9}, {3.6750580287002716`*^9, 3.675058122523638*^9}, { 3.675085338203286*^9, 3.6750853564513297`*^9}, {3.70228546198184*^9, 3.702285463069902*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Masses", "Section", CellChangeTimes->{{3.674984982123246*^9, 3.6749850024234076`*^9}}], Cell[CellGroupData[{ Cell["Ion masses", "Subsection", CellChangeTimes->{{3.6749859397170177`*^9, 3.674985961176245*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"mCl", "=", "35.453"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mBr", "=", "79.904"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mBu4N", "=", "242.463"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mBu3NMe", 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